Q. 36 I5.0( 1 Vote )

Find one-parameter families of solution curves of the following differential equations:


Answer :


Given







This is a first order linear differential equation of the form



Here, P = sec2x and Q = tan x sec2x


The integrating factor (I.F) of this differential equation is,



We have


I.F = etan x


Hence, the solution of the differential equation is,





Let tan x = t


sec2xdx = dt [Differentiating both sides]


By substituting this in the above integral, we get




Recall





yet = tet – et + c


yet × e–t = (tet – et + c)e–t


y = t – 1 + ce–t


y = tan x – 1 + ce–tan x [ t = tan x]


Thus, the solution of the given differential equation is y = tan x – 1 + ce–tan x


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz on DIfferential CalculusFREE Class
Functional Equations - JEE with ease48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses